Questions from linear algebra course

1. Create the matrix A and the demand vector D₀ for the economy shown in the table above. Then calculate the total output vector X for it.

2. Suppose the demand vector changes to

Find the consumption matrix A and the production vector X for the consumption matrix and the new demand vector.

3. If the demand for Services is increased by 1 unit, how much will the production of the Manufacturing sector have to increase in that economy to compensate? (with new demand D₁)

4. Which two sectors in that economy are most influenced by an increase of 1 unit in the demand of Services?

Please show as much work as possible. Thank you.

TABLE 1 EXCHANGE OF GOODS AND SERVICES IN THE U.S. FOR 1947 (IN BILLIONS OF 1947 DOLLARS) Total Gross Output Agriculture Manufacturing Services Open Sector Agriculture 34.69 39.24 84.56 4.92 5.62 Manufacturing 5.28 61.82 22.99 60.02 163.43 Services 219.03 10.45 25.95 42.03 130.65 40.24 D1= 60.02 130.65 TABLE 1 EXCHANGE OF GOODS AND SERVICES IN THE U.S. FOR 1947 (IN BILLIONS OF 1947 DOLLARS) Total Gross Output Agriculture Manufacturing Services Open Sector Agriculture 34.69 39.24 84.56 4.92 5.62 Manufacturing 5.28 61.82 22.99 60.02 163.43 Services 219.03 10.45 25.95 42.03 130.65 40.24 D1= 60.02 130.65